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On May 11, 2013, the chance of one moderate earthquake in Iran over the next 48 hours was reported at about 21.42%. A bettor wins $50 if it happens and pays $20 if it does not. What is the expected value of this bet?
AAbout +$5.01, an average gain per bet
BAbout -$5.01, an average loss per bet
CExactly $0, a perfectly fair bet
DAbout -$20.00, the full amount paid
Answer & Solution
Correct answer: B. About -$5.01, an average loss per bet
1. Let X be profit: +50 with probability 0.2142, or -20 with probability 0.7858.
2. Multiply and add: (50)(0.2142) + (-20)(0.7858) = 10.71 - 15.716 = -5.006.
3. Rounded to the nearest cent, this expected loss is about $5.01 per bet.
4. Option C ignores that the two payoffs are weighted unequally, and option D confuses the fixed loss amount with the weighted average.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.2 Mean or Expected Value and Standard Deviation_
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